Hexahedral mesh quality improvement via edge-angle optimization

Supplementary Material 1 Our method can successfully optimize over 50 octree-based 2 meshes, The results are showed in the following tables. 3 Table 1. Improving Quality of hex-meshes Octree-based method. We use metro tools to compute Hausdorff distance wrt. bounding box diagonal [1]. For each model, the first and second row is input and output, respectively. Model #hexes Err MSJ ASJ airplane1 4972 0.030 0.838 airplane1 4972 0.004393 0.508 0.879 airplane2 6118 0.018 0.848 airplane2 6118 0.003137 0.500 0.882 armadillo 19940 0.013 0.822 armadillo 19940 0.005380 0.238 0.839 armchair 18756 0.157 0.805 armchair 18756 0.002698 0.166 0.824 bimba 25347 0.0609 0.799 bimba 25347 0.007841 0.113 0.816 bird 4247 0.0313 0.820 bird 4247 0.011580 0.553 0.868 blade 10996 0.025 0.845 blade 10996 0.007911 0.312 0.868 block 1624 0.179 0.661 block 1624 0.016877 0.550 0.815 bone 2751 0.154 0.781 bone 2751 0.006475 0.207 0.794 ?Only capitalize first word and proper nouns in the title. ∗Corresponding author: Tel.: +1-713-743-5788; e-mail: [email protected] (Guoning Chen) Table 2. Improving Quality of hex-meshes Octree-based method. We use metro tools to compute Hausdorff distance wrt. bounding box diagonal [1]. For each model, the first and second row is input and output, respectively. Model #hexes Err MSJ ASJ botijo 15244 0.012 0.786 botijo 15244 0.012756 0.121 0.813 bottle1 10026 0.022 0.801 bottle1 10026 0.046987 0.075 0.796 bottle2 35886 0.129 0.79 bottle2 35886 0.011387 0.200 0.809 bumpy sphere 9903 0.138 0.771 bumpy sphere 9903 0.002958 0.174 0.794 bumpy torus 45619 0.0859 0.811 bumpy torus 45619 0.004873 0.102 0.825 bunny 27670 0.016 0.796 bunny 27670 0.007097 0.106 0.813 buste 19075 0.133 0.852 buste 19075 0.004503 0.161 0.862 camel 12874 0.014 0.779 camel 12874 0.006154 0.201 0.821 camille hand 12247 0.0239 0.812 camille hand 12247 0.005111 0.233 0.829 carter 33202 0.022 0.815 carter 33202 0.006637 0.102 0.830 chair 5464 0.014 0.744 chair 5464 0.013805 0.301 0.819 chair1 11686 0.018 0.843 chair1 11686 0.003276 0.313 0.859 chinese lion 43174 0.029 0.825 chinese lion 43174 0.005000 0.115 0.843 coverrear 37796 0.00849 0.783 coverrear 37796 0.002440 0.056 0.821 2 Given-name Surname etal / Computers & Graphics (2017) Table 3. Improving Quality of hex-meshes Octree-based method. We use metro tools to compute Hausdorff distance wrt. bounding box diagonal [1]. For each model, the first and second row is input and output, respectively. Model #hexes Err MSJ ASJ cup 48341 0.028 0.866 cup 48341 0.005255 0.138 0.874 cup1 36235 0.130 0.820 cup1 36235 0.003580 0.303 0.829 dancer 1473 0.011 0.777 dancer 1473 0.007419 0.553 0.852 dancer2 1385 0.013 0.722 dancer2 1385 0.016464 0.465 0.821 dancing children 25691 0.016 0.842 dancing children 25691 0.005184 0.103 0.856 david 52905 0.012 0.821 david 52905 0.008832 0.106 0.843 deckel 53658 0.0278 0.840 deckel 53658 0.002021 0.0296 0.864 deformed armadillo 25294 0.013 0.834 deformed armadillo 25294 0.008370 0.112 0.850 dente 13655 0.081 0.789 dente 13655 0.010161 0.115 0.806 dilo 4181 0.012 0.824 dilo 4181 0.007767 0.456 0.871 dino 8293 0.00575 0.742 dino 8293 0.013066 0.211 0.820 dino2 8799 0.023 0.794 dino2 8799 0.005613 0.219 0.816 dragon stand 24009 0.015 0.832 dragon stand 24009 0.004775 0.101 0.848 dragonstand2 23917 0.013 0.837 dragonstand2 23917 0.004598 0.304 0.857 dtorus 16065 0.151 0.82 dtorus 16065 0.001817 0.169 0.833 duck 4743 0.031 0.808 duck 4743 0.007509 0.239 0.820 duck2 72041 0.0237 0.795 duck2 72041 0.003092 0.159 0.815 eight 4571 0.169 0.781 eight 4571 0.004370 0.201 0.799 eros 25956 0.092 0.820 eros 25956 0.006504 0.115 0.836 fandisk 8941 0.0087 0.705 fandisk 8941 0.003459 0.010 0.753 fertility 21370 0.105 0.845 fertility 21370 0.001644 0.136 0.858 fish1 9537 0.015 0.815 fish1 9537 0.008377 0.308 0.845 fish2 7439 0.012 0.811 fish2 7439 0.009266 0.018 0.808 foot 4724 0.180 0.820 foot 4724 0.012382 0.302 0.835 gargoyle 41610 0.024 0.834 gargoyle 41610 0.005247 0.200 0.849 genus3 21468 0.013 0.790 genus3 21468 0.007322 0.114 0.807 Table 4. Improving Quality of hex-meshes Octree-based method. We use metro tools to compute Hausdorff distance wrt. bounding box diagonal [1]. For each model, the first and second row is input and output, respectively. Model #hexes Err MSJ ASJ glass1 5233 0.006 0.707 glass1 5233 0.003856 0.310 0.812 glass2 1855 0.011 0.678 glass2 1855 0.006310 0.301 0.780 grayloc 46490 0.008 0.844 grayloc 46490 0.004810 0.010 0.861 greek sculpture 9848 0.012 0.856 greek sculpture 9848 0.005529 0.138 0.874 hand 8170 0.0113 0.782 hand 8170 0.004134 0.108 0.810 head1 17433 0.121 0.816 head1 17433 0.004628 0.177 0.833 head2 27128 0.0195 0.796 head2 27128 0.006985 0.126 0.818 holes3 10140 0.274 0.827 holes3 10140 0.008802 0.305 0.836 homer 11690 0.026 0.830 homer 11690 0.005281 0.236 0.845 horse 12159 0.0123 0.796 horse 12159 0.203218 0.024 0.816 human1 7075 0.016 0.820 human1 7075 0.006544 0.450 0.863 human2 5363 0.014 0.782 human2 5363 0.022624 0.015 0.788 igea 21661 0.026 0.785 igea 21661 0.007184 0.129 0.803 insect 6780 0.008 0.805 insect 6780 0.006364 0.301 0.846 isidore horse 21695 0.017 0.830 isidore horse 21695 0.005455 0.120 0.849 joint 10118 0.020 0.811 joint 10118 0.001245 0.054 0.848 kiss 18418 0.027 0.844 kiss 18418 0.005075 0.224 0.857 kitten 12713 0.115 0.766 kitten 12713 0.010022 0.146 0.784 lion recon 11922 0.016 0.846 lion recon 11922 0.005836 0.204 0.862 master cylinder 55345 0.025 0.837 master cylinder 55345 0.004908 0.127 0.847 max 17161 0.062 0.799 max 17161 0.008424 0.119 0.815 moai 7320 0.192 0.820 moai 7320 0.009869 0.220 0.836 mouse 25110 0.0804 0.8 mouse 25110 0.003043 0.137 0.821 octa flower 26469 0.0116 0.746 octa flower 26469 0.005229 0.0124 0.782 oil pump 40227 0.0105 0.798 oil pump 40227 0.004835 0.072 0.819 oni 24787 0.036 0.819 oni 24787 0.006529 0.145 0.835 Given-name Surname etal / Computers & Graphics (2017) 3 Table 5. Improving Quality of hex-meshes Octree-based method. We use metro tools to compute Hausdorff distance wrt. bounding box diagonal [1]. For each model, the first and second row is input and output, respectively. Model #hexes Err MSJ ASJ part 8266 0.070 0.770 part 8266 0.010065 0.106 0.811 pear 4470 0.220 0.787 pear 4470 0.001373 0.238 0.803 pig 13987 0.021 0.793 pig 13987 0.005379 0.107 0.811 plate 15710 0.0214 0.804 plate 15710 0.484713 0.0254 0.844 red circular box 12247 0.0239 0.812 red circular box 12247 0.005111 0.233 0.829 retinal 6811 0.117 0.758 retinal 6811 0.003071 0.131 0.782 rocker 16608 0.108 0.865 rocker 16608 0.007742 0.241 0.874 rod 3675 0.037 0.770 rod 3675 0.009317 0.203 0.804 rolling stage 42182 0.030 0.828 rolling stage 42182 0.004066 0.127 0.842 santa 18000 0.0225 0.854 santa 18000 0.003881 0.453 0.865 screwdriver 8299 0.008 0.844 screwdriver 8299 0.004890 0.249 0.868 sculpt 20572 0.017 0.714 sculpt 20572 0.012328 0.052 0.758 sediapatch 28379 0.123 0.812 sediapatch 28379 0.007175 0.127 0.824 teaport 16888 0.022 0.793 teaport 16888 0.005232 0.108 0.810 thai statue 14635 0.013 0.852 thai statue 14635 0.006430 0.403 0.878 toy1 18947 0.121 0.806 toy1 18947 0.001506 0.201 0.823 uu-memento 194240.0165 0.802uu-memento 19424 0.002022 0.0296 0.864 venus44210.174 0.778venus4421 0.002827 0.226 0.798woodenfish 197090.010 0.796woodenfish 19709 0.008136 0.210 0.826wrench20970.0098 0.286wrench2097 0.004929 0.0174 0.513References1 [1] Guthe, M, Borodin, P, Klein, R. Fast and accurate hausdorff distance2 calculation between meshes. In: In WSCG. 2; 2005, p. 41–48.3